ECS708P (2021) Page 3 Question 2: a) The probability density function of the Gaussian distribution is given by p(x;4, 2) = (x-w7x-1(-1) (27)/2L 1/2 1 e Explain what each symbol denotes and give its dimensionality. Sketch the probability density function in the 1-dimensional case and use it to support your explanations. [8 marks] b) Fit a Gaussian distribution to the following set of 1-dimensional data X = (3,2,4,4,2,3). Show the formulas that you use for your estimation and state what is the criterion that is optimised [10 marks] c) In several cases the covariance matrix is singular and cannot be inverted. In which cases is this more likely to happen? Why is this a problem? Give a solution to it. [7 marks] Turn Over